Funded by SCOAP3We discuss a renormalization procedure for random tensor networks, and show that the corresponding renormalization-group flow is given by the Hamiltonian vector flow of the canonical tensor model, which is a discretized model of quantum gravity. The result is a generalization of the previous one concerning the relation between the Ising model on random networks and the canonical tensor model with N=2. We also prove a general theorem that relates discontinuity of the renormalization-group flow and the phase transitions of random tensor networks.